No-fives subgroup temperaments: Difference between revisions

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 [[Badness]] (Sintel): 0.0454
+=== Boethian ===
+Boethian is a [[5L 2s|diatonic-based]] temperament that makes [[513/512]] vanish, so that the major third (C–E) is ~[[24/19]] and the minor third (C–E♭) is ~[[19/16]]. As such, it functions as a 2.3.19-subgroup analogue of [[meantone]], though the small size of the comma puts it at [[schismic]] level of accuracy. In particular, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, so boethian intersects with schismic in the prime-5 infill extension thereof, called [[nestoria]], which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.
+[[Subgroup]]: 2.3.19
+[[Comma list]]: 513/512
+{{Mapping|legend=2| 1 0 9 | 0 1 -3 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2498{{c}}, ~3/2 = 701.4958{{c}}
+: [[error map]]: {{val| +0.250 -0.209 -0.501 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.3445{{c}}
+: error map: {{val| 0.000 -0.610 -1.547 }}
+{{Optimal ET sequence|legend=1| 5, 7, 12, 41, 53, 65, 77, 219, 296, 1557bhhhh, 1853bhhhh }}
+[[Badness]] (Sintel): 0.0294
 === Dog ===
@@ Line 1,174: / Line 1,194: @@
 [[Badness]] (Sintel): 0.491
-=== Boethian ===
-Boethian is a [[5L 2s|diatonic-based]] temperament that makes [[513/512]] vanish, so that the major third (C–E) is ~[[24/19]] and the minor third (C–E♭) is ~[[19/16]]. As such, it functions as a 2.3.19-subgroup analogue of [[meantone]], though the small size of the comma puts it at [[schismic]] level of accuracy. In particular, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, so boethian intersects with schismic in the prime-5 infill extension thereof, called [[nestoria]], which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.
-[[Subgroup]]: 2.3.19
-[[Comma list]]: 513/512
-{{Mapping|legend=2| 1 0 9 | 0 1 -3 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.2498{{c}}, ~3/2 = 701.4958{{c}}
-: [[error map]]: {{val| +0.250 -0.209 -0.501 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.3445{{c}}
-: error map: {{val| 0.000 -0.610 -1.547 }}
-{{Optimal ET sequence|legend=1| 5, 7, 12, 41, 53, 65, 77, 219, 296, 1557bhhhh, 1853bhhhh }}
-[[Badness]] (Sintel): 0.0294
 === Lipsett ===